Active noise cancellation (ANC) technology has been developing for many years and a range of headphones incorporating ANC technology (also known as ambient noise reduction and acoustic noise cancelling headphones) are now available on the market. ANC headphones are however often larger, heavier and require a dedicated power source in comparison to equivalent headphones that do not provide ANC functionality. Such characteristics are generally viewed negatively by consumers who generally want headphones to be small, light and the power source to last as long as possible. There is therefore a general desire to continue to reduce the size, weight and power requirements of ANC headphones whilst maintaining noise cancellation performance.
There has also been a growth in recent years in the use of wireless headphones, such as Bluetooth headphones that support an A2DP profile. Wireless headphones require circuitry to support the wireless reception of audio data and a battery to power that circuitry. Wireless headphones are therefore also generally bulkier and heavier than equivalent wired headphones and require regular recharging.
It would be desirable to offer ANC functionality in wireless headphones but using conventional technologies this would require adding additional circuitry providing the ANC functionality to wireless headphones, further increasing their size, weight and power requirements. There is therefore a need for a low-power ANC solution that can be readily incorporated in wireless headphones without significantly increasing the size and weight of the headphones.
In particular, there is a desire to incorporate ANC functionality into the wireless communication controller present in wireless headphones. And given the recent growth in the sales of Bluetooth headphones, there is a particular desire to incorporate ANC functionality into a Bluetooth controller. However, communication controllers generally do not have the characteristics suitable for implementing conventional ANC controller—typically there will be excessive delays on the digital path and low computational processing power. There is therefore a need for an ANC controller that can be implemented with low computational complexity and can operate at a processor or communications controller having significant delays on its digital path.
The central idea of ambient noise reduction headphones is illustrated in FIG. 1, in which a microphone 101 is used to capture ambient noise Ni(t) inside of the ear cup 100 that is present as a result of noise Ne(t) in the environment of the headphones. An anti-noise signal is produced by a loudspeaker 102 that has the same amplitude but opposite phase to the captured ambient noise so as to cancel out the ambient noise Ni(t) in the ear cup. e(t) is the signal captured by microphone, −c(t) is the ANC controller, and u(t) is the noise cancellation signal provided by the controller to the speaker.
Active noise cancellation can be equated to the disturbance rejection problem from control system theory, which is shown in FIG. 2 and described in “Automatic Control Systems”, 7th Ed. by B. C. Kuo and F. Golnaraghi, Prentice Hall, N.J., 1995. Comparing FIG. 2 with the headphones illustration in FIG. 1, the error signal e(t) is the signal captured by microphone 101, the controller −C(s) maps onto controller −c(t) of the noise reduction headphones (the minus signal indicates a negative feedback system), the plant P(s) is the transfer function from the input of the loudspeaker to the output of the microphone 101, and the disturbance d(t) in FIG. 2 is the ambient noise inside of the ear cup, Ni(t) in FIG. 1.
Observe that the error signal output e(t) of the control system in FIG. 2 will, in the absence of the control, be equal to d(t) or Ni(t)—i.e. no noise attenuation is achieved. The transfer function (or sensitivity function) from the disturbance signal to the error signal can be obtained,
            E      ⁡              (        s        )                    D      ⁡              (        s        )              =            1              1        +                              P            ⁡                          (              s              )                                ·                      C            ⁡                          (              s              )                                            =          S      ⁡              (        s        )            
Since the objective of this control system is good rejection of the disturbances, S(s) should be small,|1+P(s).C(s)|  1
An appropriate controller function C(s) can therefore be designed by measuring plant P(s) (it is the transfer function from the input of the loudspeaker 102 to the output of the microphone 101). This kind of controller is known as a feedback (FB) controller and its analog version, which can be designed using control theory, is suitable for use in the ANC controllers of headphones.
Broadly, there are two different arrangements used in commercial ambient noise reduction headphones: the feedback (FB) arrangement that uses a microphone 302 inside of the ear cup 301 as shown in FIG. 3A, and the feedforward (FF) arrangement that uses a microphone 303 outside of the ear cup 304 as shown in FIG. 3B. Generally, headphones with large ear cups use an FB arrangement and ear bud style headphones use the more compact FF arrangement (which does not require a microphone between the headphone speaker and the user's ear).
ANC controllers for either arrangement can be analog or digital, and fixed or adaptive. Historically, most commercial ambient noise reduction headphones have used analog, fixed controllers because digital controllers that offer sufficiently low delay characteristics to be useful as a digital ANC controller have been expensive and power hungry. For example, U.S. Pat. No. 4,455,675, describes a fixed analog feedback controller for ANC headphones.
More recently, digital controllers have become prevalent, such as the fixed digital controller described in U.S. patent application Ser. No. 2008/0310645 that can switch among three modes (feedback, feedforward and a hybrid feedback-feedforward mode) in dependence on the environmental noise characteristics. Sony Corporation have also released a pair of noise cancelling headphones that use a feedback digital controller and microphone arrangement—model MDR-NC500D.
Adaptive digital ANC controllers will now be considered that employ adaptive algorithms, such as least mean squares (LMS) or recursive least squares (RLS) algorithms. Most preferably the adaptive controller is configured to operate in accordance with an FXLMS (Filtered-Reference Least Mean Squares) algorithm, such as the algorithm described in “Signal Processing for Active Control” by S. Elliott, Academic Press, 2001, and in “Active Noise Control Systems, Algorithms and DSP Implementations” by S. M. Kuo and D. R. Morgan, John Wiley and Sons, 1996.
FIG. 4 is a block diagram of a control system representing an adaptive feedback ANC controller that uses the FXLMS adaptive algorithm with an adaptive filter and is suitable for use in the feedback arrangement shown in FIG. 3A. Signal Ni(k) represents the ambient noise inside the ear cup 301, e(k) is the error signal generated by the internal microphone 302, x(k) is the “generated” reference signal, and u(k) is the output of the adaptive filter −C(k). Typically adaptive filter −C(k) is an FIR (finite impulse response) filter whose coefficients are set in accordance with the FXLMS algorithm. P(z) represents the plant model transfer function from the input of the loudspeaker 303 to the output of the microphone 302—this can be measured from a real-world system.
Theoretical simulations of the controller can be performed once the plant transfer function P(z) of the real-world system being modeled has been measured (the plant transfer function being a mathematical representation of the convolved frequency responses of the loudspeaker and microphone, the acoustic path between loudspeaker and microphone and the characteristics of the electronics coupled to the microphone and loudspeaker). The convolution of plant P(z) with the loudspeaker input signal (u(k)) and the superposition of the convolution result with the ambient noise signal Ni(k) represents the response of the real-world system to the ambient noise signal that naturally occurs inside the ear cup of the headphones. Simulations of an ANC controller can be performed in numerical computing packages, such as MATLAB.
The objective of the adaptive controller is to adjust the coefficients of adaptive filter −C(k) in order to minimize error signal e(k). Adaptive algorithm FXLMS is used to achieve this end. The behavior of the controller shown in FIG. 4 can be described by the following set of equations. Firstly, we define e(k),e(k)=ni(k)+PT(k)·U(k)where P(k) and U(k) are column vectors with length M,P(k)=[p1(k)p2(k) . . . pM(k)]T U(k)=[u1(k)u2(k−1) . . . uM(k−M+1)]T 
Secondly, we define how the coefficients of the adaptive filter C(k) are updated so as to minimize the error e(k):C(k+1)=C(k)−μ.{circumflex over (X)}(k).e(k)where μ is the step size of the LMS algorithm and C(k) and {circumflex over (X)}(k) are column vectors given by:C(k)=[c1(k)c2(k) . . . cN(k)]T {circumflex over (X)}(k)=[{circumflex over (x)}(k){circumflex over (x)}(k−1) . . . {circumflex over (x)}(k−N+1)]T with N representing the number of coefficients of C(k).u(k), x(k) and {circumflex over (x)}(k) are given by:u(k)=XT(k).C(k)x(k)=e(k)+{circumflex over (P)}T(k).U(k){circumflex over (x)}(k)={circumflex over (P)}T(k).X(k)with X(k) a column vector given by:X(k)=[x(k)x(k−1) . . . x(k−N+1)]T 
Generally, to simplify the algorithm it is assumed that {circumflex over (P)}(z)=P(z). Algorithms other than FXLMS can be used, and several alternatives are described in the “Signal Processing for Active Control” and “Active Noise Control Systems, Algorithms and DSP Implementations” textbooks referenced above.
A feedforward adaptive controller will now be considered, which is also described in the “Signal Processing for Active Control” and “Active Noise Control Systems, Algorithms and DSP Implementations” textbooks. As illustrated in FIG. 5, for a feedforward adaptive controller, two microphones 501, 502 are generally necessary for each ear cup 500 of the headphones: an internal microphone 502 and an external microphone 501.
FIG. 6 is a block diagram of a control system representing an adaptive feedforward controller suitable for implementation at the headphones of FIG. 5. The main difference compared to the feedback system is that the reference signal x(k) is now provided by signal Ne(k) from the external microphone 501. FIG. 6 identifies a transfer function 601 between the internal and external microphones H(z), with the goal of the adaptive algorithm being to find a controller given by,C(z)=−H(z)*P(z)−1 
The equations describing the feedforward adaptive controller can be obtained from the equations describing the feedback adaptive controller by realizing that x(k) is equal to the signal from the external microphone. The internal microphone 502 is not shown in FIG. 6 because its presence is represented by e(k).
Again, the plant model P(z) can be obtained by measurement of the headphone system, which, for a digital system, typically includes: a digital to analog converter (DAC); an analog to digital converter (ADC); a DAC reconstruction low-pass filter; an ADC anti-aliasing low-pass filter; loudspeaker and microphone amplifiers; the acoustic path between loudspeaker and microphone; and the microphone and loudspeaker impulse responses.
A third variant of ANC controller is the hybrid feedforward-feedback controller. The combination of the feedforward and feedback type of controllers can achieve higher active noise attenuation than each controller type alone. Hybrid feedforward-feedback controllers are described in detail in “A New Two-Sensor Active Noise Cancellation Algorithm”, Proc. of the International Conference on Acoustic, Speed and Signal Processing, 1993; “Hybrid Feedforward-Feedback Active Control”, Proc. of the American Control Conference, Boston, 2004; and “Hybrid Active Noise Control System for Correlated and Uncorrelated Noise Sources”, Proc. of the 6th International Symposium on Image and Signal Processing and Analysis, 2009.
A schematic diagram of headphones implementing a hybrid feedforward-feedback controller are shown in FIG. 7. The headphones comprise internal and external microphones 701 and 702, respectively, within each headphone cup 700. The arrangement of the feedback and feedforward filters with respect to the inputs from the microphones and the output to the loudspeaker is shown in the figure.
An adaptive hybrid feedforward-feedback controller embodying the FXLMS adaptive algorithm is presented as a control system in FIG. 8. Both the feedback controller C_fb(k) and the feedforward controller C_ff(k) are adaptive filters whose coefficients are determined in accordance with the FXLMS algorithm. The aggregate controller arrangement can be seen to be a combination of the feedback controller shown in FIG. 4 and the feedforward controller shown in FIG. 6.
ANC controllers can be either analog or digital. For digital controllers, the delay on the digital path (which forms part of the plant model) is critical to the performance of the controller. Typically, the main contribution to the delay is from the digital signal processor (DSP). If the digital path presents a large delay, the controller will not be able to cancel a broadband signal but it can still cancel periodic signals, such as tones of fixed frequency. Such considerations led to the development of feedback hybrid analog-digital controllers, which use an analog fixed feedback controller and a digital adaptive feedback controller. Examples of this type of controller are set out in “Feedback control sound”, a PhD thesis by B. Rafael of University of Southampton, 1997, and in “A Robust Hybrid Feedback Active Noise Cancellation Headset” by Y. Song et al., IEEE Trans. On Speech and Audio Processing, Vol. 11, No. 4, Jul. 2005. These controllers can handle both broadband input signals and periodic input signals, with an analog controller being used to attenuate the broadband signals (analog filters having a short delay can be readily constructed) and a digital controller being used to attenuate the periodic input signals.
FIG. 9 shows a block diagram of the general structure of a typical feedback hybrid analog-digital controller. A microphone 101 and a loudspeaker 102 are configured at a pair of headphones as shown in FIG. 1. The signal from the microphone is amplified at pre-amp 903 to form error signal e(k), which is provided to both the analog signal path and analog controller 908, and to the digital signal path. The digital signal path comprises an anti-aliasing low-pass filter 904, an analog-to-digital controller (ADC) 907, DSP digital controller 906, digital-to-analog controller (DAC) 905 and reconstruction low-pass filter 901. The signals from the digital and analog paths are combined at 909 and provided to a power-amp 902 that drives loudspeaker 102.
Various types of conventional ANC controller have been described above. However, none of these basic controller types provide an efficient, low-complexity solution that offers excellent ANC performance yet is suitable for incorporation at a low power processor or communication controller that may include a significant delay on the digital path.